We show that MaxEnt is so rich that it can distinguish between any two different mappings: there always exists a nonnegative weight vector which assigns them different MaxEnt probabilities. Stochastic HG instead does admit equiprobable mappings and we give a complete formal characterization of them.

This paper focuses on the most basic implicational universals in phonological theory, called T-orders after Anttila and Andrus (2006). It develops necessary and sufficient constraint characterizations of T-orders within Harmonic Grammar and Optimality Theory. These conditions rest on the rich convex geometry underlying these frameworks. They are phonologically intuitive and have significant algorithmic implications.

This paper focuses on the most basic implicational universals in phonological theory, called T-orders after Anttila and Andrus (2006). It shows that the T-orders predicted by stochastic (and partial order) Optimality Theory coincide with those predicted by categorical OT. Analogously, the T-orders predicted by stochastic Harmonic Grammar coincide with those predicted by categorical HG. In other words, these stochastic constraint-based frameworks do not tamper with the typological structure induced by the original categorical frameworks.